Alterations in cerebrospinal fluid glycerophospholipids and phospholipase A2 activity in Alzheimer's disease.

Our aim is to study selected cerebrospinal fluid (CSF) glycerophospholipids (GP) that are important in brain pathophysiology. We recruited cognitively healthy (CH), minimally cognitively impaired (MCI), and late onset Alzheimer's disease (LOAD) study participants and collected their CSF. After fractionation into nanometer particles (NP) and supernatant fluids (SF), we studied the lipid composition of these compartments. LC-MS/MS studies reveal that both CSF fractions from CH subjects have N-acyl phosphatidylethanolamine, 1-radyl-2-acyl-sn-glycerophosphoethanolamine (PE), 1-radyl-2-acyl-sn-glycerophosphocholine (PC), 1,2-diacyl-sn-glycerophosphoserine (PS), platelet-activating factor-like lipids, and lysophosphatidylcholine (LPC). In the NP fraction, GPs are enriched with a mixture of saturated, monounsaturated, and polyunsaturated fatty acid species, while PE and PS in the SF fractions are enriched with PUFA-containing molecular species. PC, PE, and PS levels in CSF fractions decrease progressively in participants from CH to MCI, and then to LOAD. Whereas most PC species decrease equally in LOAD, plasmalogen species account for most of the decrease in PE. A significant increase in the LPC-to-PC ratio and PLA2 activity accompanies the GP decrease in LOAD. These studies reveal that CSF supernatant fluid and nanometer particles have different GP composition, and that PLA2 activity accounts for altered GPs in these fractions as neurodegeneration progresses.

Calculating the Malliavin derivative of some stochastic mechanics problems.

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper.